1 not in r9c9, it is in r8c7 or r8c9 (Row on 3x3 Block interaction)
3 not in r4c2, it is in r1c2 or r3c2 of the 3x3 (3x3 Block on Row/Column interaction)
3 not in r9c2, it is in r1c2 or r3c2 of the 3x3 (3x3 Block on Row/Column interaction)
3 not in r5c4, it is in r5c1 or r5c3 of the 3x3 (3x3 Block on Row/Column interaction)
3 not in r5c6, it is in r5c1 or r5c3 of the 3x3 (3x3 Block on Row/Column interaction)
3 in r9c6 3 in r8c9 - Unique Vertical

> 1 not in r9c9, it is in r8c7 or r8c9 (Row on 3x3 Block interaction)
> 3 not in r4c2, it is in r1c2 or r3c2 of the 3x3 (3x3 Block on Row/Column interaction)
> 3 not in r9c2, it is in r1c2 or r3c2 of the 3x3 (3x3 Block on Row/Column interaction)
> 3 not in r5c4, it is in r5c1 or r5c3 of the 3x3 (3x3 Block on Row/Column interaction)
> 3 not in r5c6, it is in r5c1 or r5c3 of the 3x3 (3x3 Block on Row/Column interaction)
> 3 in r9c6 3 in r8c9 - Unique Vertical

2) What is the relevance of r9c9 not having value 1?
This is a consequence of either r9c1 or r9c2 being 1 (the only
cells available in box 7 with a 1 in col3 and a 1 in row 7 already).
But, how does it affect the placement in r9c6?

3) My own approach is to test a line (row OR column) if it has six or
more "known" values (and often testing five also is fruitful).

The key to unblocking this is to know that r5c1 or r5c3 must have
value 3 and so r5c6 CANNOT have value 3. This puts a 3 in r9c6.

My own work on "Mandatory Pairs" (to be submitted shortly) would
reveal this situation almost transparently but in the absence of any
"pencil marks" -

How does one carry in one's head the sequence of

a) one of r1c2 and r3c2 must have value 3.
Thus
b) one of r5c1 and r5c3 must have value 3

at the same time as evaluating the missing items in column 6?

+++

My admiration (and marvelling) is for those who CAN hold such a
complex series of patterns simultaneously - and also who are able
to FORGET those patterns as soon as the puzzle is solved and the
need to remember them has dissipated. I know that I could LEARN
some patterns for a grid by setting up associations to put such into
longer term memory - but my need is remember the patterns only
for the next hour (hopefully less!!) and then to erase them..

Is there any technique that can be learned by others to assist in this?
Is it the same skill as is required to play bridge, for example?

a) one of r1c2 and r3c2 must have value 3.
Thus
b) one of r5c1 and r5c3 must have value 3

at the same time as evaluating the missing items in column 6?

I'm not sure how other people do it, but I just try to visualize the pattern. Pair (a) defines a vertical line, and pair (b) defines a horizontal line. I can "see" those lines just fine while I'm thinking about numbers elsewhere in the puzzle.

I don't think it's so much a question of carrying a sequence in one's head as it is of "seeing" a pattern emerge. Here's an example, from today's (10/13/05) Daily Sudoku. In this puzzle it's fairly obvious that all six of the missing "3"s can be placed right off the bat, leading to the following position:

Code:

. . . 3 . . . 5 4
9 . 3 . . . . . .
5 . . 8 6 . 2 . 3

. 3 . 7 . . . 1 .
. . 8 . . 3 4 . .
. 2 . . . 4 3 9 .

1 . 7 . 2 8 . 3 9
3 . . . . . . . 1
2 5 . . 3 7 . . .

In this position there's a pattern in the bottom row of 3x3 boxes that allows one to place four numbers into the grid almost instantaneously. Can you spot it? Look at the grid and try to visualize what I'm talking about before you read on ...

OK, here's the pattern. The pair {2, 7} appears in both row 7 and row 9 _outside_ of the bottom right 3x3 box. Therefore the pair {2, 7} must occupy the two cells r8c7 & r8c8. Therefore the "8" in the ninth row must be in the bottom right 3x3 box, leading immediately to the placement of two more "8"s -- at r8c2 and at r1c1.

It was only after I'd spotted the two "8"s in the left hand column of 3x3 boxes that I noticed the "2" at r3c7, which allowed me to resolve the {2, 7} pair in the lower right hand corner of the puzzle. Once one spots the {2, 7} pattern one can place four numbers in this puzzle all at once.